ON THE TENSOR PRODUCTS OF JC-ALGEBRAS
Copyright policy )ON THE TENSOR PRODUCTS OF JC-ALGEBRAS
AbstractIn this article we introduce and develop a theory of tensor products of JW-algebras. Since JW-algebras are so close to W*-algebras, one can expect that the W*-algebra tensor product theory will be actively involved. It is shown that if Mand N are JW-algebras with centres Z1 and Z2 respectively, then Z1 ⊗ Z2 is not the centre of the JW-tensor product JW() (see below for notation) ofMand N, in general. Also, the type decomposition of JW() has been determined in terms of the type decomposition of the JW-algebras M and N which, essentially, rely on the relationship between the types of the JW-algebra and the types of its universal enveloping Von Neumann algebra.
- King Saud University Saudi Arabia
\(JC\)-algebras, Jordan structures on Banach spaces and algebras, Nonassociative topological algebras, Abstract operator algebras on Hilbert spaces, General theory of von Neumann algebras, tensor product, tensor products of JW-algebras, General theory of \(C^*\)-algebras, enveloping \(C^*\)-algebras, Tensor products in functional analysis, Nonassociative selfadjoint operator algebras
\(JC\)-algebras, Jordan structures on Banach spaces and algebras, Nonassociative topological algebras, Abstract operator algebras on Hilbert spaces, General theory of von Neumann algebras, tensor product, tensor products of JW-algebras, General theory of \(C^*\)-algebras, enveloping \(C^*\)-algebras, Tensor products in functional analysis, Nonassociative selfadjoint operator algebras
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